The Kids Are Alright

The following is a guest post by @sunset_shazz.

Carson Wentz’s start to the 2017 season has garnered national plaudits for his stewardship of the Eagles’ league-leading offense. But it being 2017, there lurks a coterie of skeptics who claim his underlying ability is “horrendous” like Blake Bortles or merely pedestrian like Andy Dalton. Even more emphatically, poor Jared Goff was confidently pronounced a bust after one season.

Is it fair to judge a quarterback solely on his rookie year? What about after the first nine weeks of his second season in the league? And how might one systematically evaluate a developing quarterback, relative to historical data?

Let us consider some advanced metrics that are used to evaluate quarterbacks:

• Adjusted Net Yards / Attempt (ANY/A) was developed by the great Chase Stuart, and accounts for sack yards, while providing a bonus for touchdowns and a penalty for interceptions. Both Stuart and Topher Doll have shown that ANY/A predicts wins. Danny Tuccitto has brilliantly used confirmatory factor analysis to show that ANY/A is a stable indicator of QB quality.
• Defense-adjusted Value over Average (DVOA), the brainchild of Aaron Schatz at Football Outsiders, is a success-based, opponent-adjusted per-play efficiency metric intended to both correlate with non-opponent adjusted wins (descriptive) and to predict future opponent-adjusted wins.
• Defense-adjusted Yards above Replacement (DYAR) uses similar success-rate inputs to DVOA, in order to compute an aggregate value for a player (combining volume and efficiency).
• Total QBR is ESPN Stats & Information’s proprietary efficiency metric that combines both passing and running contributions, adjusted for game situation, with charting to assign responsibility to a quarterback’s receivers and blockers.

Through nine weeks, the 2017 sophomore class is playing at an extraordinarily high level, as measured by each of these advanced stats:

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Please note that nothing herein intends to argue for any of these quarterbacks to the detriment of the others. Though the data presented above is insufficiently precise to draw ordinal rankings, it is unequivocal:

Wentz is good. Goff is good. Prescott is good. All three of these things can simultaneously be true, pace internet trolls.

Some epistemic humility is in order: the first-nine-week sample size is obviously noisy, with varying degrees of luck, opponent quality, team injuries, coaching quality and supporting casts influencing the statistical performance of each QB. Danny Tuccitto warns us that ANY/A stabilizes at 326 dropbacks, and even at that sample size, 50% of the observation represents randomness/luck. Nonetheless, the broad takeaway should be that each sophomore QB has thus far performed at a top-quartile level, judged by a variety of different metrics. Is this good? And how confident can we be that such performance will continue?

Recently, Chase Stuart noted that three sophomores from the same class have not played this well since at least the NFL-AFL merger. Though ANY/A is less context-specific than the other measures, it has the advantage of being transparent and easy to calculate, permitting historical analysis. Stuart compared the first 8 weeks of 2017 for Goff, Prescott and Wentz to full seasons of prior 2nd year QBs. Comparing partial to full seasons isn’t quite neutral, due to the disparity in number of games sampled; we should expect some mean reversion of our reference QBs as sample size increases. Using pro-football-reference’s excellent query engine, I examined the first 9 weeks for each sophomore quarterback from 1999 through 2017. Historical comparisons need to be adjusted for era, due to the enormous change in average NFL passing efficiency over time. To account for this, I divided each quarterback’s ANY/A by the league average for that year. [1]

Top ANY/A vs Average since 1999, sophomore QBs, weeks 1-9

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The 76 QB sample set in this study is itself a product of survivorship bias: only those QBs who were successful enough to throw 100 passes in the first 9 weeks of their second year in the league are included. On the other side of the distribution, successful QBs who rode the pine for their first few years (like Aaron Rodgers, Tony Romo or Philip Rivers) are not in this sample. The average age of the sample is 24, similar to our reference QBs.

The three 2017 sophomores are, as Stuart observed, performing extraordinarily well relative to their peer set (all are in the top quartile of the sample). Relative to their era, they are passing with greater efficiency than Tom Brady, Drew Brees, Matt Ryan or Andrew Luck did in their second seasons.

You will also note that the top ranked sophomore QBs include many future hits (Big Ben, Kurt Warner, P. Manning) and a few notable misses (Nick Foles, Derek Anderson). The last column I included is the Career Approximate Value (CAV), which is a (very) rough method developed by Doug Drinen that puts a single number on a player’s total career, encompassing both longevity and performance.

Below, I plotted log Career Approximate Value against ANY/A relative to league average for the first 9 weeks for second year QBs from 1999-2015 (I excluded QBs from 2016-2017 because recent QBs have not yet had sufficient time to accumulate CAV points).

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The positive relationship shown above indicates that the first 9 weeks of a sophomore season predicts 37% of a QB’s future CAV. Do note that the correlation is sensitive to a few outliers. The odious Ryan Leaf and Akili Smith are on the bottom left, whereas Foles and Anderson are on the bottom right. I don’t want to ascribe an illusion of precision to this rough analysis – don’t fixate on the exact R-squared number, or the model coefficients. Both sample size and the extremely imprecise nature of CAV make me hesitant to draw definitive conclusions from the data. What is interesting to me is that the same plot using a QB’s full rookie season yields an R-squared of 0.224 – in other words, the first 9 weeks of a QB’s sophomore season tells you roughly 70% more about his future career than his entire rookie season does. Extending this analysis to full seasons since 1970, the R-squared is 0.083 and 0.2348 for rookie and sophomore years, respectively (n=155 & 204). My interpretation of this data: though rookie and second year passing efficiency predict only a small fraction of a quarterback’s career value, the sophomore year deserves 2.8x as much weight as the rookie year, in terms of confidence about predictive power. Rookie performance, in particular, is extremely noisy. One would have been wise to heavily discount Troy Aikman, Donovan McNabb and Terry Bradshaw’s dreadful rookie seasons. Rams fans should take note.

Relatedly, I didn’t find any predictive power when measuring the degree of era-adjusted-ANY/A improvement from rookie to sophomore season. This echoes Vincent Verhei’s study of second year improvement using DVOA. In hypothesis testing, a negative result can be an interesting result.

Quantitative analysis is not the only tool in an NFL researcher’s kit. Film study (though not my sphere of competence) is also valuable. Though Nick Foles had a magical sophomore season, the film showed reason for concern, as my friend Derek Sarley noted. I don’t personally see similar issues with Wentz – both his pre-snap adjustments and post-snap play appear to pass the “eye test”. No, he’s not perfect. Yes, he has flaws he needs to address. But so do all second year quarterbacks.

Moreover, our penchant for treating quarterbacks as static vessels of talent/ability shortchanges the importance of coaching and development. The installation of a new coaching regime in Los Angeles appears to be an interesting natural experiment, in terms of Goff’s maturation. Similarly, we can view Ezekiel Elliott’s probable(?) suspension as an instrumental variable when evaluating Prescott.

All inductive statements are, by their very nature, revisable. We don’t know the future; we can only use informed judgment to hazard a prediction. The false-positive rate for the top 20 QBs in table 2 above is 25% by my count [2], so let’s take that as the “base rate” of failure for the 2016 Sophomore QBs. It is therefore reasonable to expect that two – perhaps all three – of the 2016 sophomores will enjoy successful careers as NFL starters.

Finally, in these impatient times, let us remind ourselves that transcendent quarterbacks do not emerge, fully formed, from the forehead of Zeus. Each of these young, relatively inexperienced quarterbacks is playing the most technically and cognitively demanding position in sports at a very high level. Adjusted for experience and era, their achievements are even more astounding. The evidence suggests that the future of quarterback play is bright. Football fans, rejoice.

Thanks to Eagles fan / Data Scientist Sean J. Taylor for his insightful discussion on methodology. Any errors are mine alone.

[1] PFR’s partial season engine shows results from 1999 onward. Full season results go back before the merger, and also generate an era-adjusted ANY/A+ which uses a “Z-score” methodology, expressed in standard deviations above or below the population mean. My method is less sophisticated, though nonetheless robust.

[2] I excluded the reference QBs, as well as Marcus Mariota.

@sunset_shazz is an Eagles fan who lives in Marin County, California. He previously wrote about 4th down decisions.

Time To Clear The Air

The following is a guest post by @sunset_shazz.

This is a wonderful time to be an Eagles fan. Jim Schwartz’s Attack Nine defense is rapidly exorcizing the ghost of Juan Castillo. Doug Pederson has rejuvenated an offense that had become stale and predictable under Chip Kelly. And, of course, rookie quarterback Carson Wentz is turning heads across the league, not to mention in the oval office.

Eagles fans, unexpectedly blessed with success, look to the poet Browning to give voice to their collective sentiment:

The lark's on the wing; 
The snail's on the thorn: 
God's in His heaven— 
All's right with the world!

But wait. From his perch at the indispensable Football Outsiders, Scott Kacsmar has some discomfiting news: both Wentz and Cowboys rookie QB Dak Prescott are mere dink and dunkers, with lower than average air yards per attempt (defined as the average distance a football is thrown beyond the line of scrimmage). A low score on this metric is undesirable, in Kacsmar’s view.

The inimitable Jimmy Kempski responded to Kacsmar’s initial claim with a sardonic video rewind post, prompting Kacsmar, in an entertainingly vitriolic rant, to frame this argument as a contest between enlightened, statistically rigorous analysts on one side and straw-manning “numbers are for nerds” egg avatars on the other.

I don’t believe that view is correct.

As Brian Burke has explained:

A statistic that both correlates with winning and correlates with itself would be a reliable predictor of future wins.

First, you want your in-sample measure to have some predictive power in estimating out-of-sample future wins, because, hello, you play to win the game. Second, you want a metric to have some degree of statistical persistence over time, in order to be confident you are measuring a signal (in this case, an attribute of quality quarterbacking) rather than mere noise.

Regarding the latter, Kacsmar notes that in 2015, the correlation between air yards in the first three weeks of the year and the air yards for the entire season was 0.80. Well, that doesn’t seem quite fair, does it? After all, what we really care about is the correlation between the first 3 weeks of the season and the ensuing 14 weeks. Using his dataset, and using the Spearman rank correlation estimator rather than a standard Pearson estimator, which in this case would be considered less robust, I found that the correlation between the first 3 weeks and ensuing 14 weeks last year was 0.60. That’s pretty good, as far as football statistics go. However, do note that within a season a number of other factors surrounding the quarterback are, for the most part, held relatively constant: coaching scheme, strength of running game, defensive strength, etc.

When Chase Stuart examined the persistence of the Air Yards metric from year to year, he found that between 2006 and 2012 for 100 qualifying QBs the correlation between Year N and Year N+1 for Air Yards was 0.34. Both completion percentage and yards/attempt were “stickier” with N to N+1 correlations of 0.51.

Kacsmar, in his FO piece, assembles a smaller dataset (than Stuart, above) which he judges to be salient:

I gathered that yearly data on 21 quarterbacks with at least four years of starting experience, all of whom are still active starters this year except for the retired Peyton Manning. The following table shows their average air yards by year for the period of 2006 to 2015.

The first rule of Analytics Club is to plot your data, so I plotted Kacsmar’s data into a time series chart, in order to visualize the range and variability of the attribute, segregated by quarterback, over time:

Taking Kacsmar’s dataset (which, it is important to note, uses 21 quarterbacks who have experienced some career longevity rather than Stuart’s more comprehensive analysis of 100 QBs), and running a similar autocorrelative N to N+1 analysis, I found that the year-to-year correlation was 0.40. My friend, real-life data scientist Dr. Sean J. Taylor, was generous enough to both replicate my work and provide me with a scatterplot, complete with line of best fit and confidence interval shading:

Chart courtesy Sean J. Taylor

The autocorrelation statistic, the scatterplot and time series visuals each show the same thing: we are measuring mostly noise, with a faintly detectable QB signal. The attributes I mentioned before—scheme, effectiveness of the running game, defensive efficiency which affects game script—are all likely to change the calculus of decision-making with regard to throwing shallow or deep.

In fact, Kacsmar himself gives us a good reason to doubt the validity of Air Yards in capturing an attribute of QB quality: it doesn’t improve as a player gains more experience. Quarterbacks, like all athletes, typically experience an age curve, reflecting both athletic maturation and decline, as well as the steep learning curve imposed by formidable NFL defenses. Chase Stuart has shown that the age curve for NFL quarterbacks is pronounced. The absence of an “age/experience curve” for Air Yards is yet another red flag.

Air Yards doesn’t appear to measure a persistent quarterback attribute over time, particularly when compared with a conventional statistic such as completion percentage or advanced statistics such as Adjusted Net Yards / Attempt (ANY/A, for which Danny Tuccitto brilliantly used confirmatory factor analysis to verify its validity) or Defensive Yards Above Replacement (DYAR, rigorously developed and tested by Aaron Schatz).

But does it predict wins?

My general model of the production function of football is as follows: runs and passes are inputs; completions and first downs are intermediate goods; points are outputs. Success rate metrics such as Defensive-Adjusted Value Over Average (DVOA), DYAR, and ANY/A are all measures of intermediate goods which are of interest to the analyst because they tend to reliably convert to points. And as Chip reminds us, if you (f__king) score points you are more likely to win. 

Chart courtesy Sean J. Taylor

The scatterplot above shows the relationship between a QB’s average air yards over a season and the points scored by his team over that season. There is no statistically significant relationship between the two measures. Contrast this with ANY/A, which correlates 0.55 with wins. Or DYAR & DVOA, whose parameters were specified in order to predict future wins.

Kacsmar has been careful to note that he isn’t an advocate of maximizing Air Yards; he thinks middle is best. He elaborates in his FO piece:

Generally, air yards are a stat where you don't want to rank at the bottom, because that is where many ineffective passers dwell, including Blaine Gabbert. That preference for short throws often extends to crucial downs, which is why these quarterbacks tend to do poorly in ALEX and attacking the sticks. However, it is not preferable to rank at the very top in air yards either, because that is how "screw it, I'm going deep" players such as Michael Vick, Tim Tebow, Vince Young and Rex Grossman have earned their reputation as inefficient passers.

His claim, if I have understood it correctly, is that quarterbacks at the tails of the distribution are less likely to be successful in future. Our scatterplot above doesn’t show any relationship between the middle of the distribution and success, measured by points scored. But could Kacsmar’s anecdotal observation that “middle is best” be a mere artifact of sampling? If successful quarterbacks have longer careers, the law of large numbers dictates that they will, by mere virtue of larger samples, be less prone to the extremes in Air Yards. Taking a separate dataset evaluating quarterback air yards between 1992 and 2012, and plotting those against passes thrown, one arrives at the following:

You can see that the more passes a given quarterback throws, the less variance he exhibits with respect to his peer cohort. This needs to be examined further, in my view. I admit that I am not familiar with the nuances surrounding various measures of air yards (various observers have different estimates), but a longer, broader dataset would be desirable to plot air yards versus attempts. We don’t want to fall prey to the famous Bill and Melinda Gates Foundation misstep where it was initially claimed that small schools are consistently among the best performing schools, when it was merely the case that small schools experience more variance than larger schools, and therefore disproportionately comprise the tails of the distribution.

Here is the plot of the fourth-grade math scores versus number of students in the school:

The prior two sections showed that Air Yards as a measure is neither statistically persistent nor predictive of success, in terms of points scored. I did mention some alternative, robust metrics, two of which are generated by Football Outsiders. As of Week 3, FO has not applied opponent adjustments to their measures. On a raw Value Over Average and Yards Above Replacement measure, these young QBs have performed in the top quartile over the first 3 games.

Looking merely in the rearview mirror, without making any judgments about the future, they appear to have performed well.

Another measure I have mentioned, Adjusted Net Yards / Attempt (the “adjustment” gives a bonus for touchdowns and a penalty for interceptions, and the “net” deducts sack yards) is a persistent, predictive measure. With a hat tip to the excellent Derek Sarley, I prefer to plot this against completion %, to show both efficiency and consistency of per-play execution (weeks 1-3, minimum 46 attempts):

Once again, the rookies have played impressively: Wentz and Prescott are in the top quartile (4th and 8th, respectively) in ANY/A and the 2nd quartile (13th and 10th, respectively) in completion %.

As Bill Barnwell has noted, the statistics from 3 games tell us very little about how a QB will play in the future. A very small sample size disadvantages a purely statistical analysis; the comparative advantage shifts towards the film analyst. Ideally, one would combine both, but in this case, the stats aren’t meaningfully more robust than mere anecdotes. This is why I disagree with Kacsmar’s adversarial Michael Lewis-style “stats versus scouts” framing; the NFL stats on these two rookies don’t really tell you anything dispositive yet. From a purely Bayesian perspective, the eye test is just as likely as a mere three weeks of quantitative data to meaningfully update one’s priors. I have not yet enjoyed the privilege of watching Prescott, but I’ve seen every Wentz throw; moreover, I’ve seen astute film analysts such as Greg Cosell, Fran Duffy, Jimmy Kempski and Ryan from ChipWagon break his film down. Lastly, as Brent from EaglesRewind notes, one’s priors should be heavily influenced by draft position, which was the NFL auction market’s initial “revealed preference” view of value.

As for me, I’m on the Wentz Wagon. Dan McQuade reasons persuasively that Eagles fans should enjoy this run, because life is fleeting. Memento mori, football fans.

TL;DR:

• The early results from the credible advanced statistics, meaning those that tend to be both persistent and predictive, are that Wentz and Prescott have played well in their first three games.
• Looking at the numbers alone, a three game stretch is insufficient to give us high confidence that such success will continue in future. 
• The Air Yards statistic is neither persistent nor predictive, and reflects the aesthetic tastes of one particular writer, rather than a desirable quarterback attribute.

Thanks to Sean J. Taylor for his methodological insight and scatterplot work. Any errors are mine alone.

@sunset_shazz is a Philadelphia Eagles fan who lives in Marin County, California. He previously wrote about Chip Kelly's Oregon bias and other topics, and contributed to the 2015 Eagles Almanac.